UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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Conference: Bucharest University Faculty of Physics 2003 Meeting


Section: Theoretical Physics and Applied Mathematics Seminar


Title:
Spinning Particles and Dirac-type Operators on Curved Spaces


Authors:
Mihai Visinescu


Affiliation:
Depart.Theoretical Physics

National Institute for Physics and Nuclear Engineering, Magurele, Bucharest, Romania


E-mail


Keywords:


Abstract:
We review the geodesic motion of pseudo-classical particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. From the covariantly constant Killing-Yano tensors of this space we construct three new Dirac-type operators which are equivalent with the standard Dirac operator. Finally the Runge-Lenz operator for the Dirac equation in this background is expressed in terms of the forth Killing-Yano tensor which is not covariantly constant. As a rule the covariantly constant Killing-Yano tensors realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. On the other hand, the not covariantly constant Killing-Yano tensors are important in generating hidden symmetries. The presence of not covariantly constant Killing-Yano tensors implies the existence of non-standard supersymmetries in point particle theories on curved background. References: M. Visinescu, Int. Journ. Mod. Phys. A17,1049 (2002) I. I. Cotaescu, M. Visinescu, hep-th/0301108 I. I. Cotaescu, M. Visinescu, Gen. Rel. Grav. 35, 389 (2003) I. I. Cotaescu, M. Visinescu, Journ. Math. Phys. 43, 2978 (2002) I. I. Cotaescu, M. Visinescu, Class. Quant. Grav. 18, 3383 (2001) I. I. Cotaescu, M. Visinescu, Phys. Lett. B502, 229 (2001)